Sure! Let's determine the radius of a circle that passes through the point [tex]\((-4, 3)\)[/tex].
1. Identify the coordinates: The point given is [tex]\((-4, 3)\)[/tex].
2. Identify the center of the circle: Since no specific center is mentioned, we will assume that the center of the circle is at the origin, [tex]\((0, 0)\)[/tex].
3. Formula for the radius: The radius [tex]\(r\)[/tex] can be found using the distance formula between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]. In this case, the points are [tex]\((0, 0)\)[/tex] and [tex]\((-4, 3)\)[/tex].
The distance formula is given by:
[tex]\[
r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
4. Plug in the values:
[tex]\[
r = \sqrt{(-4 - 0)^2 + (3 - 0)^2}
\][/tex]
5. Simplify the expression:
[tex]\[
r = \sqrt{(-4)^2 + 3^2}
\][/tex]
[tex]\[
r = \sqrt{16 + 9}
\][/tex]
[tex]\[
r = \sqrt{25}
\][/tex]
6. Calculate the square root:
[tex]\[
r = 5
\][/tex]
So, the radius of the circle passing through the point [tex]\((-4, 3)\)[/tex] is [tex]\(5\)[/tex].
Answer: None of the options (A, B, C, D) are correct, as the radius is [tex]\(5\)[/tex].
